{"id":"https://openalex.org/W2528061142","doi":"https://doi.org/10.37236/6493","title":"Independent Sets in the Union of Two Hamiltonian Cycles","display_name":"Independent Sets in the Union of Two Hamiltonian Cycles","publication_year":2018,"publication_date":"2018-12-21","ids":{"openalex":"https://openalex.org/W2528061142","doi":"https://doi.org/10.37236/6493","mag":"2528061142"},"language":"en","primary_location":{"id":"doi:10.37236/6493","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6493","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p48/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059026447","display_name":"Ron Aharoni","orcid":"https://orcid.org/0000-0002-1768-1901"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Ron Aharoni","raw_affiliation_strings":["Technion"],"affiliations":[{"raw_affiliation_string":"Technion","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031540948","display_name":"D\u00e1niel Solt\u00e9sz","orcid":"https://orcid.org/0000-0002-1668-748X"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Daniel Solt\u00e9sz","raw_affiliation_strings":["MTA R\u00e9nyi Institute"],"affiliations":[{"raw_affiliation_string":"MTA R\u00e9nyi Institute","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059026447"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03778888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7889300584793091},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7033308148384094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6755386590957642},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6201632022857666},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6019096374511719},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.5135076642036438},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47378990054130554},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4476904273033142}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7889300584793091},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7033308148384094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6755386590957642},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6201632022857666},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6019096374511719},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.5135076642036438},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47378990054130554},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4476904273033142},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/6493","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6493","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:real.mtak.hu:97054","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1609.09746","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.09746","pdf_url":"https://arxiv.org/pdf/1609.09746","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2528061142","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1609.09746","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1609.09746","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.09746","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/6493","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6493","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1134778232","display_name":null,"funder_award_id":"K-120706","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G1748000517","display_name":null,"funder_award_id":"NKFIH","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G3114978053","display_name":null,"funder_award_id":"K-108947","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G3252451321","display_name":null,"funder_award_id":"KH-126853","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G8414776512","display_name":null,"funder_award_id":"120706","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G899848074","display_name":null,"funder_award_id":"108947","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"}],"funders":[{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null},{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2528061142.pdf","grobid_xml":"https://content.openalex.org/works/W2528061142.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2074920973","https://openalex.org/W2272753335"],"related_works":["https://openalex.org/W3000684470","https://openalex.org/W2567763580","https://openalex.org/W1980411478","https://openalex.org/W2293176046","https://openalex.org/W2984019183","https://openalex.org/W1984537817","https://openalex.org/W2963107223","https://openalex.org/W3109316666","https://openalex.org/W2747893514","https://openalex.org/W2091201408","https://openalex.org/W2086587080","https://openalex.org/W3210829833","https://openalex.org/W3172394114","https://openalex.org/W2023434610","https://openalex.org/W1993252920","https://openalex.org/W2746511447","https://openalex.org/W2527484120","https://openalex.org/W2021936327","https://openalex.org/W2103269371","https://openalex.org/W2741199816"],"abstract_inverted_index":{"Motivated":[0],"by":[1,23,88,190],"a":[2,42,64,73,78,89,135,150,170],"question":[3],"on":[4,31,93,97,173],"the":[5,14,19,25,57,121,130,143,153,157,177],"maximal":[6,26],"number":[7,27,155,158],"of":[8,28,46,59,67,124,145,159,164,179],"vertex":[9],"disjoint":[10],"Schrijver":[11],"graphs":[12,140],"in":[13,56,107],"Kneser":[15],"graph,":[16],"we":[17,133],"investigate":[18],"following":[20],"function,":[21],"denoted":[22],"$f(n,k)$:":[24],"Hamiltonian":[29,147,181],"cycles":[30,40,148,182],"an":[32],"$n$":[33],"element":[34],"set,":[35],"such":[36,81],"that":[37,82,114,141,168],"no":[38],"two":[39,146,180],"share":[41],"common":[43],"independent":[44],"set":[45],"size":[47],"more":[48],"than":[49],"$k$.":[50],"We":[51,71,112],"shall":[52],"mainly":[53],"be":[54,188],"interested":[55],"behavior":[58],"$f(n,k)$":[60],"when":[61],"$k$":[62],"is":[63,86,104,126,167,176],"linear":[65],"function":[66],"$n$,":[68,98],"namely":[69],"$k=cn$.":[70],"show":[72],"threshold":[74],"phenomenon:":[75],"there":[76],"exists":[77],"constant":[79,90],"$c_t$":[80,125],"for":[83,100,139],"$c&lt;c_t$,":[84],"$f(n,cn)$":[85,103],"bounded":[87],"depending":[91],"only":[92],"$c$":[94],"and":[95,99,156,183],"not":[96,127],"$c_t":[101],"&lt;c$,":[102],"exponentially":[105],"large":[106],"$n":[108],"~(n":[109],"\\to":[110],"\\infty)$.":[111],"prove":[113,134],"$0.26":[115],"&lt;":[116,118],"c_t":[117],"0.36$,":[119],"but":[120],"exact":[122],"value":[123],"determined.":[128],"For":[129],"lower":[131],"bound":[132],"technical":[136],"lemma,":[137],"which":[138],"are":[142],"union":[144,178],"establishes":[149],"relation":[151],"between":[152],"independence":[154],"$K_4$":[160,192],"subgraphs.":[161,193],"A":[162],"corollary":[163],"this":[165],"lemma":[166],"if":[169],"graph":[171],"$G$":[172],"$n&gt;12$":[174],"vertices":[175],"$\\alpha(G)=n/4$,":[184],"then":[185],"$V(G)$":[186],"can":[187],"covered":[189],"vertex-disjoint":[191]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
